淮北师范大学信息学院 2025 届学士学位论文 利用导数解题的综合分析和探讨讨论系 别: 数 学 系 专 业: 数学与应用数学 学 号: 202518084001 姓 名: 柴 先 红 指 导 教 师: 王 慧 指导老师职称: 讲 师 2013 年 5 月 10 日利用导数解题的综合分析和探讨讨论柴先红（淮北师范大学信息学院，安徽 淮北，23500）摘 要导数时近代数学的基础，时数学分析课程中重要的基础概念之一；是讨论客观世界物质运动变化的有力工具，在现代化建设的各个领域中有着广泛的应用，自然对中学数学也有着重要的指导作用.本文就从五个方面来介绍导数在中学数学中的应用，运用导数的思想方法和基本理论来解决数学中有关函数性质的讨论及其应用、数列前项之和、不等式的证明、应用题求解等问题.既为解决初等数学的某些问题找到了一些新的途径，又使导数对初等数学的知道作用得到具体说明.需要再修改！关键词：导数, 应用, 函数，数列，不等式，初等数学Derivative Comprehensive Analysis and Discussion of Research to Solve ProblemsChai Xianhong(Huaibei normal university college of information, huaibei, 23500)Abstract Derivative as the basis of modern mathematics, the mathematical analysis is one of the important basic concepts in the course; Is the study of the objective world powerful tool, change of material movement in modern construction has been widely used in every field, nature also has an important guiding role for middle school mathematics. This paper from five aspects, introduces the application of derivative in the middle school mathematics, based on the idea of derivative method and basic theory to solve in mathematics, a discussion about the nature of the function and application, the sequence of the sum referred to in the preceding paragraph, the inequality proof, such as word problem solving problems. Some elementary mathematics to solve the problems found out some new way, and the derivative of elementary mathematics know role for specific instructions.Keyword...
